We revisit the problem of generating synthetic data under differential privacy. To address the core limitations of marginal-based methods, we propose the Private Adaptive Generative Adversarial Network with Bayes Network Structure ($\texttt{PrAda-GAN}$), which integrates the strengths of both GAN-based and marginal-based approaches. Our method adopts a sequential generator architecture to capture complex dependencies among variables, while adaptively regularizing the learned structure to promote sparsity in the underlying Bayes network. Theoretically, we establish diminishing bounds on the parameter distance, variable selection error, and Wasserstein distance. Our analysis shows that leveraging dependency sparsity leads to significant improvements in convergence rates. Empirically, experiments on both synthetic and real-world datasets demonstrate that $\texttt{PrAda-GAN}$ outperforms existing tabular data synthesis methods in terms of the privacy–utility trade-off.